Pro-Ject 1- which sonos product should I BT to?

If you are using the Amp for surrounds, then you will not be able to connect the turntable to it in order to have audio play through the rest of your speakers. This is because the line in and sub outputs are disabled.

There are a few ways to get audio through your system through.

1. A Port would be the best solution that can be configured to auto play to the HT system 
2. Era 100 which is the least expensive speaker solution. You will need the official Sonos USB C to aux adapter for this
3. A used Connect S15 that will do the same thing as the Port.

I have not suggested Bluetooth because for the best sound a hardwired connection is the best solution.

Have a look at this page from the Sonos support site for more information:

https://support.sonos.com/en-us/article/listen-to-your-turntable-on-sonos

The only Bluetooth capable unit you own is the Move Gen. 1, and although you can connect the turntable to the Move via Bluetooth, it doesn’t have the capability to share Bluetooth input with the rest of the system. 

Thought Amp was a BT option? Then could connect Arc?

The Amp does not have BT capability. And as ​@Pools-3015 suggests, if it’s set up as a surround driver, bonded to the Arc, all external inputs are turned off, other than the surround signal.